Ann, You haven't said whereabouts in the world you are, which would narrow the possibilities down quite a bit. ChrysN's squirrel suggestion sounds very possible. I've seen one at it and they can be very neat about it.

I don't know if you have them in your part of the universe, but where I live armadillos will do this kind of damage. They like to dig down and eat grubs, roots, and anything else they can find. If it is an armadillo, about all you can do is trap it in a live animal trap and release it in the neighborhood of someone you don't like.

I've seen squirrels do that with tulip bulbs. They may be the ones responsible. Maybe they didn't like the taste of lilies so they left it. If you do a google search for 'how to stop squirrels from digging up bulbs" you'll see that others have had this problem.